Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT135 °C85 °C10 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 135 to 85 °C while the cold fluid heats from 10 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 85 °CTc: 10 → 25 °C
ΔTlm = K
2.Easy
lengthT120 °C85 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 120 to 85 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 85 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT145 °C105 °C20 °C70 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 400 kW. Its heat transfer area is 12 m². The hot fluid cools from 145 to 105 °C and the cold fluid heats from 20 to 70 °C. Find the overall heat transfer coefficient U.

Q̇ = 400 kWA = 12 m²Th: 145 → 105 °CTc: 20 → 70 °C
U = W/(m²·K)
4.Medium
lengthT140 °C115 °C30 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 130 kW. The hot fluid cools from 140 to 115 °C and the cold fluid heats from 10 to 30 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWU = 800 W/(m²·K)Th: 140 → 115 °CTc: 10 → 30 °C
A = m²
5.Hard
lengthT130 °C10 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 8 m² and U = 2000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 8 m²U = 2000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
6.Hard
lengthT90 °C50 °C72.85 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 90 to 50 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 90 → 50 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 88.56 K
  2. 2. Tc,out = 18.79 °C
  3. 3. U = 471.5 W/(m²·K)
  4. 4. A = 1.512 m²
  5. 5. Tc,out = 96.5 °C
  6. 6. A = 24 m²

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